Abstract: The aim of this paper is to investigate a multiresolution analysis of nested subspaces of trigonometric polynomials. The pair of scaling functions which span the sample spaces are fundamental functions for Hermite interpolation on a dyadic partition of nodes on the interval . Two wavelet functions that generate the corresponding orthogonal complementary subspaces are constructed so as to possess the same fundamental interpolatory properties as the scaling functions. Together with the corresponding dual functions, these interpolatory properties of the scaling functions and wavelets are used to formulate the specific decomposition and reconstruction sequences. Consequently, this trigonometric multiresolution analysis allows a completely explicit algorithmic treatment.

[15]A.
F. Timan, Theory of approximation of functions of a real
variable, Translated from the Russian by J. Berry. English translation
edited and editorial preface by J. Cossar. International Series of
Monographs in Pure and Applied Mathematics, Vol. 34, A Pergamon Press Book.
The Macmillan Co., New York, 1963. MR
0192238